Relational Encryption

1. A method comprising: receiving a first linearity ciphertext that represents a first biometric template of non-uniformly distributed first biometric data processed to a level of randomness associated with a security parameter and encrypted using a relational linearity encryption scheme; receiving a second linearity ciphertext that represents a second biometric template of non-uniformly distributed second biometric data processed to the level of randomness associated with the security parameter and encrypted using the relational linearity encryption scheme; receiving a first proximity ciphertext that represents the first biometric template of the first biometric data processed to the level of randomness associated with the security parameter and encrypted using a relational proximity encryption scheme; receiving a second proximity ciphertext that represents the second biometric template of the second biometric data processed to the level of randomness associated with the security parameter and encrypted using the relational proximity encryption scheme; determining a proximity relationship between the first proximity ciphertext and the second ciphertext using a proximity relational secret key; as part of determining the proximity relationship, determining a linearity relationship between the first linearity ciphertext and the second linearity ciphertext using a linearity relational secret key; and authenticating an identity of a user based upon the security parameter, the linearity relationship, and the proximity relationship.

2. The method of claim 1 , wherein the processing to the level of randomness is performed by a linear extractor.

3. The method of claim 1 , wherein the biometric data has characteristics of entropy, noise threshold, and domain.

4. The method of claim 3 , wherein the processing to the level of randomness is dependent on one or more of the characteristics.

5. The method of claim 1 , wherein the first biometric data has a correlation with another biometric characteristic and the processing to the level of randomness accounts for the correlation.

6. The method of claim 1 , wherein the security parameter for the authenticating is proportional to the level of randomness.

7. The method of claim 1 , further comprising: storing the second linearity ciphertext as a registration linearity ciphertext associated with the user; storing the second proximity ciphertext as a registration proximity ciphertext associated with the user; and receiving and storing the linearity relational secret key and the proximity relational secret key.

8. A non-transitory computer-readable medium having encoded therein programming code executable by a processor to perform or control performance of operations comprising: receiving a first linearity ciphertext that represents a first biometric template of non-uniformly distributed first biometric data processed to a level of randomness associated with a security parameter and encrypted using a relational linearity encryption scheme; receiving a second linearity ciphertext that represents a second biometric template of non-uniformly distributed second biometric data processed to the level of randomness associated with the security parameter and encrypted using the relational linearity encryption scheme; receiving a first proximity ciphertext that represents the first biometric template of the first biometric data processed to the level of randomness associated with the security parameter and encrypted using a relational proximity encryption scheme; receiving a second proximity ciphertext that represents the second biometric template of the second biometric data processed to the level of randomness associated with the security parameter and encrypted using the relational proximity encryption scheme; determining a proximity relationship between the first proximity ciphertext and second ciphertext using a proximity relational secret key; as part of determining the proximity relationship, determining a linearity relationship between the first linearity ciphertext and the second linearity ciphertext using a linearity relational secret key; and authenticating an identity of a user based upon the security parameter, the linearity relationship, and the proximity relationship.

9. The computer-readable medium of claim 8 , wherein the processing to the level of randomness is performed by a linear extractor.

10. The computer-readable medium of claim 8 , wherein the biometric data has characteristics of entropy, noise threshold, and domain.

11. The computer-readable medium of claim 10 , wherein the processing to the level of randomness is dependent on one or more of the characteristics.

12. The computer-readable medium of claim 8 , wherein the first biometric data has a correlation with another biometric characteristic and the processing to the level of randomness accounts for the correlation.

13. The computer-readable medium of claim 8 , wherein the security parameter for the authenticating is proportional to the level of randomness.

14. The computer-readable medium of claim 8 , further comprising: storing the second linearity ciphertext as a registration linearity ciphertext associated with the user; storing the second proximity ciphertext as a registration proximity ciphertext associated with the user; and receiving and storing the linearity relational secret key and the proximity relational secret key.

15. A method comprising: receiving biometric data, the biometric data non-uniformly distributed; processing the biometric data to a level of randomness as a plaintext vector, the level of randomness associated with a security parameter; encrypting the plaintext vector using a relational linearity encryption scheme to generate a linearity ciphertext representative of the plaintext vector; encrypting the plaintext vector using a relational proximity encryption scheme to generate a proximity ciphertext representative of the plaintext vector; communicating the linearity ciphertext and the proximity ciphertext to an authentication server; and receiving, from the authentication server, an authentication signal based on the security parameter indicative of a proximity relationship between the proximity ciphertext and a registration proximity ciphertext determined using a relational proximity key, and as part of the proximity relationship, a linearity relationship between the linearity ciphertext and a registration linearity ciphertext determined using a relational linearity key.

16. The method of claim 15 , wherein the processing the biometric data is performed by a linear extractor.

17. The method of claim 15 , wherein the biometric data has characteristics of entropy, noise threshold, and domain.

18. The method of claim 17 , wherein the processing the biometric data is dependent on one or more of the characteristics.

19. The method of claim 15 , wherein the biometric data has a correlation with another biometric characteristic and the processing the biometric data accounts for the correlation.

20. The method of claim 15 , wherein the security parameter is proportional to the level of randomness.